Phase coherence of pairs of Cooper pairs as quasi-long-range order of half-vortex pairs in a two-dimensional bilayer system

Abstract

It is known that the loss of phase coherence of Cooper pairs in two-dimensional (2D) superconductivity corresponds to the unbinding of vortex-antivortex pairs with the quasi-long-range order (quasi-LRO) in the order-parameter phase field, described by the Berezinskii-Kosterlizt-Thouless (BKT) transition of a 2D XY model. Here we show that the second-order Josephson coupling can induce an exotic superconducting phase in a bilayer system. By using tensor-network methods, the partition function of the 2D classical model is expressed as a product of 1D quantum transfer operator, whose eigen-equation can be solved by an algorithm of matrix product states rigorously. From the singularity shown by the entanglement entropy of the 1D quantum analogue, various phase transitions can be accurately determined. Below the BKT phase transition, an inter-layer Ising long-range order is established at $T_{Ising}$, and the phase coherence of both intra-layers and inter-layers is locked together. For two identical layers, the Ising transition coincides with the BKT transition at a multi-critical point. For two inequivalent layers, however, there emerges an intermediate quasi-LRO phase ($T_{Ising}<T<T_{BKT}$), where the vortex-antivortex bindings occur in the layer with the larger intra-layer coupling, but only half-vortex pairs with topological strings exist in the other layer, corresponding to the phase coherence of pairs of Cooper pairs. So our study provides a promising way to realize the charge-4e superconductivity in a bilayer system.

6 pages, 5 figures, 1 table, further revised version

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• Tensor network approach to the fully frustrated XY model on a kagome lattice with a fractional vortex-antivortex pairing transition
• Nematic Superconductivity and Its Critical Vestigial Phases in the Quasi-crystal
• Vestigial singlet pairing in a fluctuating magnetic triplet superconductor: Applications to graphene moiré systems
• High-order Time-Reversal Symmetry Breaking Normal State
• Emergent topological ordered phase for the Ising-XY Model revealed by cluster-updating Monte-Carlo method
• Observation of a Bilayer Superfluid with Interlayer Coherence
• Exactly Solvable Model of Randomly Coupled Twisted Superconducting Bilayers
• Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves
• Detecting Phase Coherence of 2D Bose Gases via Noise Correlations
• Helicity modulus in the bilayer XY model by worm algorithm
• Two-stage melting of an inter-component Potts long-range order in two dimensions
• Fate of Berezinskii-Kosterlitz-Thouless Paired Phase in Coupled $XY$ Models
• Crossover in the Ordered Phase in the Non-Mermin-Wagner-Hohenberg Regime of Spin Models with Long-Range Coupling
• Superfluid dome in the spatially modulated two-dimensional XY model